Question

Christine randomly pulls a marble from a bowl. There are 140 marbles in the bow, of which 80 are black, 28 are green, and the rest are blue.(4 points)
Determine the probability of selecting each of the given colors below. Enter the probability as a simplified fraction, unless it can be written as a whole number.

P(black) =


P(green) =


P(blue) =

P(red) =

Answer 1

To determine the probability of selecting each color of marble, we first need to find the total number of marbles and the number of marbles of each color.

1. **Total marbles** = 140
2. **Number of black marbles** = 80
3. **Number of green marbles** = 28
4. **Number of blue marbles** = Total marbles - (black marbles + green marbles)

Calculating the number of blue marbles:
\[
\text{Number of blue marbles} = 140 - (80 + 28) = 140 - 108 = 32
\]

Now we can calculate the probabilities for each color.

### Probability of selecting a black marble \( P(\text{black}) \):
\[
P(\text{black}) = \frac{\text{Number of black marbles}}{\text{Total marbles}} = \frac{80}{140} = \frac{8}{14} = \frac{4}{7}
\]

### Probability of selecting a green marble \( P(\text{green}) \):
\[
P(\text{green}) = \frac{\text{Number of green marbles}}{\text{Total marbles}} = \frac{28}{140} = \frac{2}{10} = \frac{1}{5}
\]

### Probability of selecting a blue marble \( P(\text{blue}) \):
\[
P(\text{blue}) = \frac{\text{Number of blue marbles}}{\text{Total marbles}} = \frac{32}{140} = \frac{16}{70} = \frac{8}{35}
\]

### Probability of selecting a red marble \( P(\text{red}) \):
Since there are no red marbles in the bowl, the probability will be:
\[
P(\text{red}) = 0
\]

### Final Answers:
- \( P(\text{black}) = \frac{4}{7} \)
- \( P(\text{green}) = \frac{1}{5} \)
- \( P(\text{blue}) = \frac{8}{35} \)
- \( P(\text{red}) = 0 \)